chemart / brusselator

hub:
  repo_type: generator
  builtin: brusselator
  tags:
  - banzhaf-yamamoto
chemistries:
- id: brusselator
  name: Brusselator
  intuition: 'The minimal oscillator, and the standard first test for anything that handles reaction networks.
    Two species are held constant as reservoirs, two are dynamic, and the autocatalytic step 2X + Y ->
    3X provides the feedback. Push the parameter b past 1 + a^2 and the steady state loses stability:
    concentrations stop settling and run around a limit cycle instead. The trimolecular step is chemically
    unrealistic and deliberately so - it buys analytic tractability.

    '
  origin: Prigogine & Lefever, 1968
  book: 17.4.2, 19.3; ARMS 9.4
  refs:
  - '[675]'
  family: application
  kind: generator
  constructive: false
  S:
    repr: A, B (buffered), X, Y (dynamic), D, E (waste)
    definition: explicit
  R:
    definition: explicit
    arity:
    - 1
    - 2
    - 3
    scheme: A --k1--> X ; B + X --k2--> Y + D ; 2X + Y --k3--> 3X ; X --k4--> E
  A:
    reactor:
    - ode
    - ssa
    dilution: A and B held constant by buffering
  params:
  - name: a
    type: float
    default: 1.0
    min: 0
    role: population
    meaning: '[A], held constant'
  - name: b
    type: float
    default: 3.0
    min: 0
    role: population
    meaning: '[B], held constant; sustained oscillations require b > 1 + a^2 when all k_i = 1'
  - name: k1
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: A -> X
  - name: k2
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: B + X -> Y + D
  - name: k3
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: 2X + Y -> 3X
  - name: k4
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: X -> E
  provides:
  - topology
  - stoichiometry
  - catalysts
  - rate-constants
  - initial-state
  fidelity: book
  decisions:
  - 'Buffered species A and B are listed in extras.buffered: their concentrations stay at a and b although
    the reactions consume them. Initial X, Y, D, E are 0, as in figure 17.6.'
  phenomena:
  - limit-cycle oscillations for b > 1 + a^2 (all k_i = 1); damped oscillations to (X, Y) = (a, b/a) below
  notes: The trimolecular step 2X + Y -> 3X is physically unrealistic; the book keeps it because it simplifies
    the analysis. A good test that Chemart handles arity-3 reactions and the associated l_i! factor in
    the k->c conversion.